CBSE Class 10 Mathematics Probability MCQs Set 12

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Chapter 14 Probability

Explore reliable objective questions for Chapter 14 Probability tailored for Class 10 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Practice Chapter 14 Probability MCQs for Class 10 Mathematics

View or download the dedicated Chapter 14 Probability MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: Two dice are thrown together. The probability that the difference of the numbers shown is 1 is
(a) \( \frac{3}{16} \)
(b) \( \frac{5}{18} \)
(c) \( \frac{7}{36} \)
(d) \( \frac{7}{18} \)
Show Answer & Explanation

Answer: (b) \( \frac{5}{18} \)

Explanation:
1. Total outcomes = 36.
2. Favourable: (1,2), (2,1), (2,3), (3,2), (3,4), (4,3), (4,5), (5,4), (5,6), (6,5), that is 10.
3. Probability = \( \frac{10}{36}=\frac{5}{18} \).

Teacher's Note:
1. List the pairs in an orderly way.
2. Count (1,2) and (2,1) as different outcomes.

Question 2: A book of 100 pages is opened at random. The probability that the page number is a doublet (11, 22, ... ) is
(a) \( \frac{8}{25} \)
(b) \( \frac{9}{100} \)
(c) \( \frac{7}{100} \)
(d) \( \frac{11}{100} \)
Show Answer & Explanation

Answer: (b) \( \frac{9}{100} \)

Explanation:
1. Doublet pages: 11, 22, 33, 44, 55, 66, 77, 88, 99, that is 9 pages.
2. Probability = \( \frac{9}{100} \).

Teacher's Note:
1. Doublet means both digits are the same.
2. Do not count 00 or 100.

Question 3: A factory has 120 workers, of whom 90 are female. Another 15 male workers are then employed. A worker is picked at random. The probability that the worker is female is
(a) \( \frac{3}{4} \)
(b) \( \frac{4}{9} \)
(c) \( \frac{2}{3} \)
(d) \( \frac{1}{2} \)
Show Answer & Explanation

Answer: (c) \( \frac{2}{3} \)

Explanation:
1. Total workers = 120 + 15 = 135 and female workers = 90.
2. Probability = \( \frac{90}{135} \) = \( \frac{2}{3} \).

Teacher's Note:
1. Add the new workers to the total.
2. Female workers stay at 90.

Question 4: A box contains marbles numbered 18 to 38. A marble is picked at random. The probability that its number is a multiple of 3 is
(a) \( \frac{3}{5} \)
(b) \( \frac{7}{20} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{1}{3} \)
Show Answer & Explanation

Answer: (d) \( \frac{1}{3} \)

Explanation:
1. Total marbles = 38 − 18 + 1 = 21.
2. Multiples of 3: 18, 21, 24, 27, 30, 33, 36, that is 7.
3. Probability = \( \frac{7}{21} \) = \( \frac{1}{3} \).

Teacher's Note:
1. Count both ends when numbering.
2. Simplify the fraction.

Question 5: One card is drawn from a well-shuffled deck of 52 cards. I. P(diamond) = 1/2. II. P(ace of hearts) = 1/52. III. P(not a heart) = 3/4. IV. P(king or queen) = 1/26. Which statements are true?
(a) I and II
(b) II and III
(c) III and IV
(d) none of these
Show Answer & Explanation

Answer: (b) II and III

Explanation:
1. P(diamond) = 13/52 = 1/4, so I is false.
2. P(ace of hearts) = 1/52 and P(not a heart) = 39/52 = 3/4, so II and III are true.
3. P(king or queen) = 8/52 = 2/13, so IV is false.

Teacher's Note:
1. Check each statement separately.
2. A deck has 13 cards in each suit.

Question 6: A letter is chosen at random from the letters of the English alphabet. The probability that it is a letter of the word DELHI is
(a) \( \frac{1}{5} \)
(b) \( \frac{1}{26} \)
(c) \( \frac{5}{26} \)
(d) \( \frac{21}{26} \)
Show Answer & Explanation

Answer: (c) \( \frac{5}{26} \)

Explanation:
1. DELHI has 5 different letters out of 26.
2. Probability = 5/26.

Teacher's Note:
1. Count the distinct letters.
2. The alphabet has 26 letters.

Question 7: A two-digit number is selected at random. The probability that it is a multiple of 3 and not a multiple of 5 is
(a) \( \frac{2}{15} \)
(b) \( \frac{4}{15} \)
(c) \( \frac{1}{15} \)
(d) \( \frac{4}{90} \)
Show Answer & Explanation

Answer: (b) \( \frac{4}{15} \)

Explanation:
1. Two-digit numbers: 90. Multiples of 3: 12 to 99, that is 30. Multiples of 15: 15, 30, ..., 90, that is 6.
2. Favourable = 30 − 6 = 24, so probability = 24/90 = 4/15.

Teacher's Note:
1. Remove the multiples of both 3 and 5 (multiples of 15).
2. Simplify the fraction.

Question 8: One number is selected at random from the one-digit prime numbers. The probability that it is even is
(a) \( \frac{1}{2} \)
(b) \( \frac{1}{4} \)
(c) \( \frac{4}{9} \)
(d) \( \frac{2}{5} \)
Show Answer & Explanation

Answer: (b) \( \frac{1}{4} \)

Explanation:
1. One-digit primes: 2, 3, 5, 7. Only 2 is even.
2. Probability = 1/4.

Teacher's Note:
1. List the one-digit primes first.
2. 2 is the only even prime.

Question 9: The probability of getting a number greater than 2 when a die is thrown is
(a) \( \frac{2}{3} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{4}{3} \)
(d) \( \frac{1}{4} \)
Show Answer & Explanation

Answer: (a) \( \frac{2}{3} \)

Explanation:
1. Favourable numbers: 3, 4, 5, 6, that is 4 out of 6.
2. Probability = 2/3.

Teacher's Note:
1. Count the numbers greater than 2.
2. A probability can never exceed 1.

Question 10: In a lottery there are 5 prizes and 20 blanks. The probability of getting a prize is
(a) \( \frac{2}{5} \)
(b) \( \frac{4}{5} \)
(c) \( \frac{1}{5} \)
(d) 1
Show Answer & Explanation

Answer: (c) \( \frac{1}{5} \)

Explanation:
1. Total tickets = 5 + 20 = 25.
2. Probability = 5/25 = 1/5.

Teacher's Note:
1. Total outcomes = prizes + blanks.
2. Simplify the fraction.

Question 11: Two coins are tossed together. The probability of getting at most one head is
(a) \( \frac{1}{4} \)
(b) \( \frac{1}{2} \)
(c) \( \frac{3}{4} \)
(d) 1
Show Answer & Explanation

Answer: (c) \( \frac{3}{4} \)

Explanation:
1. Outcomes: HH, HT, TH, TT. At most one head: HT, TH, TT, that is 3.
2. Probability = 3/4.

Teacher's Note:
1. 'At most one' includes zero heads.
2. Only HH is excluded.

Question 12: An urn contains 6 blue balls and a green balls. If the probability of drawing a green ball is double the probability of drawing a blue ball, then a =
(a) 6
(b) 18
(c) 24
(d) 12
Show Answer & Explanation

Answer: (d) 12

Explanation:
1. P(green) = a/(a + 6) and P(blue) = 6/(a + 6).
2. a = 2 × 6 = 12.

Teacher's Note:
1. Both probabilities have the same denominator.
2. So the numerators are in the same 2 : 1 ratio.

Free study material for Mathematics

Practice MCQs for Class 10 Mathematics Chapter 14 Probability

Chapter MCQs with Answers for Class 10 Mathematics

Review structured objective questions for Class 10 Mathematics Chapter 14 Probability. Built according to official CBSE guidelines, these MCQ sets support daily revision and core concept reinforcement.

Expert Practice Material for Class 10 Mathematics

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FAQs

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Probability MCQs Set 12 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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